I would not prune either plant until the dying parts have completely gone black. In both cases, they are probably taking nutrients out of the leaves and traps that are fading out.

One time last summer I tried trimming all the half-dead leaves off my D. capensis, and it seemed to weaken the plant. Since then I try to let nature take its course, and the plant looks much healthier.

However, if you notice any mold growing on the dead parts, I'd cut that dead tissue off right away.

Alright. Thanx!